Mechanism for producing motions representing a function of two independent variables in calculating apparatus



FOR PRODUCING MOTIONS REPRESENTING A FUNCTION OF TWO INDEPENDENT VARIABLES IN CALCULATING APPARATUS June 26, 1923.

A. BARR ET AL 1921 Z-Sheets-Sheet 2 NEGHANI SH Filed Aug. 26

FGIS.

@fr wpmw Patented June 26, 1923.

UNITED STATES PATENT OFFICE.

ARCHIBALD BARR AND WILLIAM STROUD, 0F ANNIESLAND, GLASGOW, SCOTLAND.

ASSIGNORS T0 BARR AND STROUD, LIMITED, 0F ANNIESLAN'D, GLASGOW, SCOT- LAND,

I MECHANISM FOR PRODUCING MOTIONS REPRESENTING A FUNCTION OF TWO INDE- PENDENT VARIABLES IN CALCULATING APPARATUS.

Serial No. 495,548,

(GRANTED UNDER THE PROVISIONS 0F THE ACT 0F MARCH 3, 1921, 41 STAT. L., 1313.)

To all wiz-0m 'it may concern:

Be it known that we, ARCHIBALD BARR and )VILLTAM STRoUD, subjects of the King of Great Britain and Ireland, and both of Anniesland, Glasgow, Scotland, have invented new and useful improvements in or connected with mechanism for producing motions representing a function of two independent variables in calculating apparatus, (for which we have filed application in Great Britain, May 16, 1918, Patent No. 126,798), of which the following is a specilication.

One of the objects of our invention, which relates to improvements in or connected with mechanism for producing motions representing` a function of two independent variables in calculating apparatus, is to provide improved means for obtaining a rapid mechanical solution of the equation azf 1 especially for gunner-y purposes, though the means to be described can be utilized for a very large number of other purposes where rapidity is desired.

In anti-aircraft gunnery when the two independent variables, height and angle of sight, are known, tangent elevations for a given height can be mechanically determined by employing what will be termed a twodimensional-cam constructed and so arranged that when turned about its axis, according to the magnitude of the angle of sight, a Contact member resting on the surface of the cam and guided to move, say, radially, shall move in accordance with the tangent elevation it is desired to indicate. Thus, for a given number of selected heights a corresponding number of cams suitably constructed might be provided, and if these were all mounted on a shaft in their ap-` propriate positions and the spaces between them filled in with material and smoothed off, so that one cam merged gradually into the next, we would get what will be termed a three-dimensional-cam in which the radial tangent elevations. for heights, within restricted limits, comprising a three-dimensional-cam and a contact member capable relatively of axial adjustment, is already known. Disadvantages, however, appertain to apparatus of this kind, amongst which may be mentioned the following :-(1) The variation in radial distance is very limited unless the cams are of very considerable size. (2) The steepness of the surface is frequently too great to enable axial adjustment, between the contact member and cam, to be made by sliding the one relatively to the other when the radial distance is to be increased, in consequence of its being necessary for the point of contact to be capable of lateral displacement in two directions at right angles to one another on the surface of the cam, in addition to the radial movement required which approximately is atright angles to the plane in which the lateral movements occur. This disadvantage is partly due to the fact that it is not easy to provide means, such as a roller, approximately fiictionless in two directions, at right angles to one anothenR-y The object of our present invention is to provide mechanism for producing effects of the character appertaining to those obtainable by means of a three-dimensional-cam, whereby advantages are obtained, amongst which may be enumerated the following (1) The changes in radial distance may be considerable, and (2) a Contact member is provided subject to displacement laterally in one instead of two directions.

Mechanism according to this invention consists in providing a beam capable of lateral deformation in a direction approximately at right angles to its surface, the deformation of which is produced at a number of positions in its length by means consisting each of mechanism of two-dimensional-cam character, associated with a contact member adapted to bear against the distance of any point on the surface from lthe axis is a function of two independent variables viz, the axial position of the point land the angular position of the cam.

50 Apparatus for mechanically determining surface of the beam and guided to move in a direction parallel or approximately so to the direction of movement imparted by the cam mechanism in effecting the deformation, with provision for effecting the longitudinal adjustment of the contact member on the beam relative to the positions of deformation.

Some examples illustrating methods of and the construction of mechanism for carrying our invention into practice as applied to mechanically indicate tangent elevations, will now be described.

In one case the beam provided may consist of a slightly flexible lath whose form is controlled at a suitable number of points along its length by rods whose radial extensions from a common axis are capable of alteration. At any particular moment the form of this lath corresponds, say, to the value of the tangent elevation at various heights for one particular angle of sight. If the angle of sight is altered all these controllingrods undergo appropriate changes in radial extension so that the new form which the lath assumes corresponds to the values of the tangent elevation for the new angle of sight. Thus, a particular point of the lath (corresponding to a particular height) will move in or out appropriately with the changes in the value of the angle of sight to give the correct tangent elevation. Thus, if we have a roller whose axis is perpendicular to the plane containing the central line of the lath for picking up the position on the lath at any point it need only be approximately frictionless in the direction of the length of the lath (co-rresponding to changes in height) because changes in the values of the angle of sight are not accompanied by motions of the surface parallel to the axis of the roller.

In place of a flexible lath the beam employed may be composed of a number of links hinged together, the points of control being situated at or near the hinges.

As means of control at the selected points of the beam we may employ (1) ordinary two-dimensional-cams and these may now be comparatively steep because rollers may be interposed between the beam and each of the cams, the axes of these rollers being more or less parallel to the axis of the cams. In the case of radially moving rods we may use (2) complementary spiral toothed gears A1 and B1, A2 and B2, etc., for each of the points of control t-hus, e. g.,-- A1 A2, etc., may all be fixed on the angle of sight shaft while B1 B2, etc., are mounted freely on a parallel shaft. Attached to the face of each of these spirals B1 B2 there may be fixed a toothed wheel gearing with a suitably guided rack forming the lower part of one of the control rods, or (3) we may use a special device to be presently described which is very suitable for the present purpose, or (4) we may use any suitable known device for producing variable motions.

The special device (3) which forms one `of the features of the present invention may be described in one of its forms, as follows :-The spindle of the jockey element of a differential gear is fixed to, say, the angle of sight shaft, the other two elements E and E1 are driven by the jockey but the relative motions of E and E1 at any moment are controlled\by a rocking lever with a fixed axis and carrying two pins P and P1 engaging in suitably cut scrolls on the faces of E and E1 respectively, thus P engages with E and P1 with E1. In this way at one period all the motion imparted to the jockey may be used to drive E while E1 is kept stationary or all the motion of the jockey may drive E1 while E is stationary or any fraction of the motion may drive E while the remainder drives E1. Thus we may convert a uniform motion of the angle of sight shaft into a variable motion of E or E1 (say, E, in which case E1 is used as a reservoir as it were for absorbing the undesired motion). By means of a toothed wheel fixed to E and a guided rack engaging therewith we may control the position of one of the points of the beam. Instead of having the controlling scrolls on the faces of E and E1, we may arrange them on the surfaces of two cylinders fixed to or gearing with E and E1 respectively. In this case the pins P and P1 engaging with E and E1 respectively may be fixed to a bar which can slide freely parallel to the axis or axes on which E and E1 are mounted.

In the majority of cases where threedimensional-cams are required (at all events for gunnery purposes) as one or other of the independent variables increases the indication to be obtained increases (or decreases), i. e., it does not increase, then decrease and possibly increase again. In the general case, however, of the solution of the equation 5:7 (m, y) it is necessary to provide for this contingency. This may be done by incorporating a. negative element in the gear, e. g., in case (3) above supposing the quantity t0 be indicated with increasing angle of sight instead of diminishing continuously, attained a minimum and then began to increase. In this case we could fix a pinion upon the angle of sight shaft in association with one 0r all of the differential gears described. A second guided rack gearing with this pinion placed parallel to the guided rack, the first, but on the opposite side of the shaft would provide the requisite negative element in which case the motion affecting the .controlled point of the beam mightv be derived from the motion of the centre of another pinion lying between and gearing with the racks. Thel first rack thus always moves, say, upward and the second rack downwards with an increasing value of the angle of sight. Ordinarily the first rack moves upwards faster than the second rack moves, downward so that the associated pinion moves upwards. If now the velocity of the first rack is reduced below that of the second the pinion will move downwards as is required for the particular object in view.

Some examples of construction will now be described with reference to the accompanying drawings, in which Fignre 1 is an elevation and Figure 2 is a side view of a mechanism comprising three two-dimensional-cams. Figure 3 is an elevation illustrating a modification. Figure 4 is an elevation illustrating further modifications, and Figure 5 is a side view illustrating mechanism comprising rollers and showing a method of guiding the axes of the rollers radially. Figure 6 is an elevation and Figure 7 is a side view illustrating anl arrangement in which spiral gears, wheels and racks are employed. Figure 8 is an elevation, Figure 9 is a side view, and Figure 10 is a plan illustrating a special form of variable motion cam control with a negative element incorporated, and Figure 11 is an elevation illustrating a modification thereof.

Assuming that the purpose of the gear is to exhibit tangent elevation in terms of angle of sight and height and taking the case of Figure 1 the angle of sight is set by the rotation of the shaft A, in accordance with a scale of angles of sight, upon which there are fixed by way of example three two-dimensional-cams 1, 2 and 3, against the surfaces of which there is pressed a suitably guided beam consisting of a flexible lath C upon which there rests a. contact member comprising a roller 5 whose spindle is mounted on a rod 6 sliding in a frame 7 fixed to a nut 9 which is mounted upon a screw 8. The height is set off by the rotation o-f screw 8, in accordance with a. scale of heights, which translates the roller 5 to the right or left. The tangent elevation to be exhibited will be indicated by the relative position of the parts 6 and 7. If it is desired to exhibit the value of the tangent elevation by means of a dial and pointer we may arrange that a rack is formed on the front or back of 6, such rack gearing with a long pinion rod placed parallel to 8, this pinion rod being arranged to move a dial with reference to a. fixed pointer.

In Figure 3, the beam consists of a, series of jointed links C1, C2, C3, C4, each joint being supported by the edge of one of the cams 1, 2 or 3.

In cases where the form of the cams may be very steep we may arrange rollers 4 between the cams and the beam, see Figures 4 and 5. A method of guiding the rollers 4 is shown in side view in Figure 5 which shows a Scott-Russell arrangement for securing linear motion of the centre of roller 4. This figure also illustrates the way in which the two rollers 5 and 4 co-operate in reducing friction in the two dimensions desired.

In Figures 6 and 7 are shown arrangements where the desired radial motions of the points controlling the beam are considerable. In this case spiral toothed gears A1, A2, A3, fixed to shaft A gear with complementary spiral toothed gear wheels B1, B2, B3, loose on shaft B. Fixed to B1, B2, B3, respectively are ordinary toothed wheels D1, D2, D3, gearing with racks G1, G2, G1, which support the beam, not shown in these views, at three points.

A special gear for producing variable motion having a device for introducing a. negative element in the gear will now be described with reference to Figures 8, 9 and 10. In Figure 8 the spindle of the jockey element J of a differential gear E J E1 is fixed to shaft A so that as this shaft is rotated the two bevels E and E1 tend to rotate in the same sense. Fixed to E and E1 are discs F and F1 respectively in which are cut scrolls K and K1, see Figure 9, of differing shapes. Pins P and P1 fixed to a rocking lever L control the relative motions of F and F1 and consequently of E and E1, so that for a given angular motion of A at any part of the travel we take whatever motion we desire from the part E while the residue is taken up by the part E1. The rotation of the part E might communicate motion directly to a rack by means of a pinion but in the construction illustrated a negative element is added on to the motion by means of a differential gear. In this case a pinion wheel 16 is fixed to shaft A and gears with pinion wheel 17 having a fixed spindle. The latter gears with a wheel 18 havin internal teeth and a bevel wheel 19 is xed to 18. A bevel wheel 21 is fixed to E and F, and the spindle of a jockey element 2() of the differential gear 19, 20, 21 is mounted upon toothed wheel 22 gearing with rack 23. Thus as shaft A is turned bevel wheell 21 turns with the shaft but at the prescribed rate determined by the scrolls K, K1, while bevel wheel 19 rotates in the opposite direction to that of shaft A being driven by the gear 16, 17, 18, so that at any part of the travel we can make the rack 23 gearing with 22 move up or down in the manner required.

Figure shows in elevation another method of effecting the same purpose. In, this case the spindle of J fixed to Shaft A tends to drive E and E1 in the same sense. Disc F (with scroll) and toothed Wheel 31 are fixed to E while F1 (with scroll) and 32 are fixed to E1. Toothecl wheel 31 gears with rack 41 and toothed wheel 32 with rack 42. The broad pinion 50 gearing with racks 41 and 42 and suitably guided can now be arranged to move in the prescribed manner in a plane at right angles to its axis and be arranged to impart the motion of its spindle to one point of the beam.

In certain cases we may use one type of gear to control one point of the beam and a different type of gear to control another part. In many cases too it will be necessary to control the beam at more than three points.

lVe claim l. Mechanism for producing motions representing a function of two independent variables comprising a beam capable of lateral deformation in a direction at or approximately at right angles to its surface, means for producing lateral deformation of the beam at a number of positions in its length, a contact member adapted to bear against the surface of the beam, means for guiding the Contact member in a` direction parallel or approximately so to the direction of movement imparted in effecting the deformation, and means for affecting the longitudinal adjustment of the Contact member on the beam relative to the positions o-f deformation, for thepurposes set forth.

2. Mechanism for produc-ing motions representing a function o-f two independent variables comprising a beam capable of lateral deformation in a direction at or approximately at right angles to its surface, twodimensional cams for producing lateral deformation of the beam at a number of positions in its length, a contact member adapted to bear against the surface of the beam, means for guiding the contact member in a direction parallel or approximately so to the direc-tion of movement imparted by the twodimensional cams, and means for effecting the longitudinal adjustment of the contact member on the beam relative to the positions of deformation, for the purposes set forth.

3. Mechanism for producing motions representing a function of two independent variables comprising a beam incapable of appreciable endwise movement and capable of lateral deformation in a direction at or approximately at right angles to its surface, two-dimensional cams for producing lateral deformation of the beam at a number of positions in its length, one cam at each position, a contact member adapted to bear against the surface of the beam, means for guiding the contact member in a direction parallel or approximately so to the direction of movement imparted by the twodimensional cams, and means for effecting the longitudinal adjustment of the contact member on the beam relative to the positions of deformation, for the purposes set forth.

4. Mechanism for producing motions representing a function of two independent variables comprising a beam composed of a number of links hinged together so as to be capable of lateral deformation in a direction at or approximately at right angles to its surface, means for producing lateral deformation o-f the beam at the hinged positions, a contact member adapted to bear against the surface of the beam, means for guiding the contact member' in a direction parallel or approximately so to the direction of movement imparted in effecting the deformation, and means for effecting the longitudinal adjustment of the contact member on the beam relative to the positions of deformation, for the purposes set forth.

5. Mechanism for producing motions representing a function of two independent variables comprising a beam composed of a number of links hinged together, the axes of the hinges being parallel with the surface of the beam, the beam being incapable of appreciable endwise movement, means for producing lateral deformation of the beam at the hinged positions, a contact member adapted to bear against the surface of the beam, means for guiding the contact member in a direction parallel or approximately so to the direction of movement imp-arted in effecting the deformation, and means for effecting the longitudinal adjustment of the contact member on the beam relative to the positions of deformation for the purposes set forth.

ARCHIBALD BARR. VILLIAM STR-OUD. 

